Reward functionals, salvage values, and optimal stopping
Reward functionals, salvage values, and optimal stopping
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DOI：
10.1007/s001860100161
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发表时间：
2001-12
影响因子：
1.2
通讯作者：
L. Alvarez
中科院分区：
文献类型：
--
作者：
L. Alvarez
我们考虑线性扩散的最佳停止问题的累积项测量的预期累积现值的连续的和潜在的状态依赖的利润流和即时支付测量的残值或终端价值在最佳选择的停止日期。我们推导出一个明确的表示的价值函数的极小r-过度的映射考虑扩散，并通过应用经典的线性扩散理论和普通的非线性规划技术的最佳停止状态的一组必要条件。我们还陈述了一组条件，在这些条件下，我们的必要条件也是充分的，并证明了光滑粘贴原理直接从我们的方法中得出，而相反的情况不一定为真。
We consider the optimal stopping of a linear diffusion in a problem subject to both a cumulative term measuring the expected cumulative present value of a continuous and potentially state-dependent profit flow and an instantaneous payoff measuring the salvage or terminal value received at the optimally chosen stopping date. We derive an explicit representation of the value function in terms of the minimalr-excessive mappings for the considered diffusion, and state a set of necessary conditions for optimal stopping by applying the classical theory of linear diffusions and ordinary non-linear programming techniques. We also state a set of conditions under which our necessary conditions are also sufficient and prove that the smooth pasting principle follows directly from our approach, while the contrary is not necessarily true.